gaokao 2022 Q21

gaokao · China · national-A-science 12 marks Applied differentiation Existence and number of solutions via calculus
Given the function $f ( x ) = \frac { e ^ { x } } { x } - \ln x + x - a$.
(1) If $f ( x ) \geq 0$, find the range of values for $a$;
(2) Prove that if $f ( x )$ has two zeros $x _ { 1 }$ and $x _ { 2 }$, then $x _ { 1 } x _ { 2 } < 1$.
Given the function $f ( x ) = \frac { e ^ { x } } { x } - \ln x + x - a$.\\
(1) If $f ( x ) \geq 0$, find the range of values for $a$;\\
(2) Prove that if $f ( x )$ has two zeros $x _ { 1 }$ and $x _ { 2 }$, then $x _ { 1 } x _ { 2 } < 1$.